erweitern (x^2+x-1)^5

Lösung

erweitern

(x^{2} + x - 1)^{5}

x^{10} + 5 x^{9} + 5 x^{8} - 10 x^{7} - 15 x^{6} + 11 x^{5} + 15 x^{4} - 10 x^{3} - 5 x^{2} + 5 x - 1

Schritte zur Lösung

(x^{2} + x - 1)^{5}

(x^{2} + x - 1)^{5} = (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1)

= (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1)

Multipliziere aus

(x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) (x^{2} + x - 1) : x^{10} + 5 x^{9} + 5 x^{8} - 10 x^{7} - 15 x^{6} + 11 x^{5} + 15 x^{4} - 10 x^{3} - 5 x^{2} + 5 x - 1

= x^{10} + 5 x^{9} + 5 x^{8} - 10 x^{7} - 15 x^{6} + 11 x^{5} + 15 x^{4} - 10 x^{3} - 5 x^{2} + 5 x - 1

s im pl i f y (5 + 5 c) (20 - 15 c)

e x p an d 2 π (363 + 72)

e x p an d \frac{18}{( 2 x + 3 ) x}

e x p an d \frac{2}{( t ^{2} + 2 ) ^{2}}

e x p an d \frac{7 ( 6 - 5 )}{31}